7/8y-4=15/16y+1

Solution for 7/8y-4=15/16y+1 equation:

7/8y-4=15/16y+1

We move all terms to the left:

7/8y-4-(15/16y+1)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 16y+1)!=0

y∈R


We get rid of parentheses

7/8y-15/16y-1-4=0

We calculate fractions


112y/128y^2+(-120y)/128y^2-1-4=0

We add all the numbers together, and all the variables

112y/128y^2+(-120y)/128y^2-5=0

We multiply all the terms by the denominator


112y+(-120y)-5*128y^2=0

Wy multiply elements

-640y^2+112y+(-120y)=0

We get rid of parentheses

-640y^2+112y-120y=0

We add all the numbers together, and all the variables

-640y^2-8y=0

a = -640; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-640)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-640}=\frac{0}{-1280}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-640}=\frac{16}{-1280}
=-1/80
$